Sum
The sum is the total of all the data values. The sum is also used in statistical calculations, such as the mean and standard deviation.
Mean
The mean is the average of the data, which is the sum of all the observations divided by the number of observations.
Interpretation
Use the mean to describe the sample with a single value that represents the center of the data. Many statistical analyses use the mean as a standard measure of the center of the distribution of the data.
Symmetric
Not symmetric
For the symmetric distribution, the mean (blue line) and median (orange line) are so similar that you can't easily see both lines. But the non-symmetric distribution is skewed to the right.
StDev
The standard deviation is the most common measure of dispersion, or how spread out the data are about the mean. The symbol σ (sigma) is often used to represent the standard deviation of a population, while s is used to represent the standard deviation of a sample. Variation that is random or natural to a process is often referred to as noise.
Because the standard deviation is in the same units as the data, it is usually easier to interpret than the variance.
Interpretation
Use the standard deviation to determine how spread out the data are from the mean. A higher standard deviation value indicates greater spread in the data. A good rule of thumb for a normal distribution is that approximately 68% of the values fall within one standard deviation of the mean, 95% of the values fall within two standard deviations, and 99.7% of the values fall within three standard deviations.
Hospital 1
Hospital 2
Hospital discharge times
Administrators track the discharge time for patients who are treated in the emergency departments of two hospitals. Although the average discharge times are about the same (35 minutes), the standard deviations are significantly different. The standard deviation for hospital 1 is about 6. On average, a patient's discharge time deviates from the mean (dashed line) by about 6 minutes. The standard deviation for hospital 2 is about 20. On average, a patient's discharge time deviates from the mean (dashed line) by about 20 minutes.
Minimum
The minimum is the smallest data value.
In these data, the minimum is 7.
| 13 | 17 | 18 | 19 | 12 | 10 | 7 | 9 | 14 |
Interpretation
Use the minimum to identify a possible outlier or a data-entry error. One of the simplest ways to assess the spread of your data is to compare the minimum and maximum. If the minimum value is very low, even when you consider the center, the spread, and the shape of the data, investigate the cause of the extreme value.
Maximum
The maximum is the largest data value.
In these data, the maximum is 19.
| 13 | 17 | 18 | 19 | 12 | 10 | 7 | 9 | 14 |
Interpretation
Use the maximum to identify a possible outlier or a data-entry error. One of the simplest ways to assess the spread of your data is to compare the minimum and maximum. If the maximum value is very high, even when you consider the center, the spread, and the shape of the data, investigate the cause of the extreme value.
Range
The range is the difference between the largest and smallest data values in the sample. The range represents the interval that contains all the data values.
Interpretation
Use the range to understand the amount of dispersion in the data. A large range value indicates greater dispersion in the data. A small range value indicates that there is less dispersion in the data. Because the range is calculated using only two data values, it is more useful with small data sets.
Median
The median is the midpoint of the data set. This midpoint value is the point at which half the observations are above the value and half the observations are below the value. The median is determined by ranking the observations and finding the observation that are at the number [N + 1] / 2 in the ranked order. If the number of observations are even, then the median is the average value of the observations that are ranked at numbers N / 2 and [N / 2] + 1.
For this ordered data, the median is 13. That is, half the values are less than or equal to 13, and half the values are greater than or equal to 13. If you add another observation equal to 20, the median is 13.5, which is the average between 5th observation (13) and the 6th observation (14).
Interpretation
Symmetric
Not symmetric
For the symmetric distribution, the mean (blue line) and median (orange line) are so similar that you can't easily see both lines. But the non-symmetric distribution is skewed to the right.
Sum of Squares
The uncorrected sum of squares are calculated by squaring each value in the column, and calculates the sum of those squared values. For example, if the column contains x1, x2, ... , xn, then sum of squares calculates (x12 + x22 + ... + xn2). Unlike the corrected sum of squares, the uncorrected sum of squares includes error. The data values are squared without first subtracting the mean.
Total Count
The total number of observations in the column. Use to represent the sum of N missing and N nonmissing.
| Total count | N | N* |
|---|---|---|
| 149 | 141 | 8 |
N
The number of non-missing values in the sample.
| Total count | N | N* |
|---|---|---|
| 149 | 141 | 8 |
N*
The number of missing values in the sample. The number of missing values refers to cells that contain the missing value symbol *.
| Total count | N | N* |
|---|---|---|
| 149 | 141 | 8 |
